Chebyshev''s inequality, Advanced Statistics

Chebyshev's inequality: A statement about the proportion of the observations which fall within some number of the standard deviations of the mean for any of the probability distribution. One description is that for the random variable, X is given as follows

218_Chebyshev’s inequality.png 

here k is the number of standard deviations, σ, from the mean, µ. For instance, the

inequality states that at least 75% of observations fall within the two standard deviations of the mean. If the variable X can take on only the positive values as follows, basically known as the Markov inequality, holds;
1515_Chebyshev’s inequality1.png

 

 

 

Posted Date: 7/26/2012 6:18:19 AM | Location : United States







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